Factions are the only ones capable of producing, the average freelancer that owns a factory, would have to ask a faction [of the right type Weapon/Droids/Ships/Items/Vehicles] to manage it for him/her, and to allow him/her to join that faction to produce.

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1.2.1/ What are the requirements to produce?

The manager must:

* Be a production faction of the right type (See Production: Production Faction Types).
* Have sufficient credits to pay for production.
....

The person starting production and the operator must be in the faction that is the manager and have either Level 1 or 2 'Production' privilege.